Impact of Neighboring Chains on Torsional Defects in

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Impact of Neighboring Chains on Torsional Defects in Oligothiophenes Elizabeth C. Vujanovich, Jacob W. G. Bloom, and Steven E. Wheeler* Department of Chemistry, Texas A&M University, College Station, Texas 77842, United States S Supporting Information *

ABSTRACT: Conjugated organic oligomers are central to the development of efficient organic electronic devices and organic photovoltaics. However, the torsional flexibility of many of these organic materials, in particular oligothiophenes, can adversely affect charge transfer properties. Although previous studies have examined the torsional flexibility of oligothiophenes, there have been only limited studies of the effects of interchain interactions on their torsional potentials. B97-D/ TZV(2d,2p) was first benchmarked against a CCSD(T)/ aug-cc-pVTZ torsional potential for bithiophene as well as SCS-MP2/TZVPP interaction energies for noncovalent sexithiophene (6T) dimers. The effect of neighboring chains on three distinct torsional modes of sexithiophene was studied using B97-D. Complexation with one or more neighboring chains has a dramatic effect on each of these torsional potentials. For example, for two stacked chains, alternated twisting motions are competitive with torsion about a single terminal dihedral angle, and in both cases we predict nonplanar global energy minima and large amplitude torsional motions at room temperature. In other words, the presence of a single neighboring chain induces significant deviations from planarity in oligothiophenes. However, in the environment of crystalline 6T, the trend in predicted torsional potentials match those of isolated chains, but the force constants associated with torsional motions increase by an order of magnitude. Consequently, although individual oligothiophene chains are torsionally flexible and model stacked dimers exhibit extreme deviations from planarity, in crystalline 6T these oligomers are predicted to adopt planar configurations with a steep energetic cost associated with torsional defects. solution.15 Volden et al.13 reported electron diffraction structures of both the syn (with a C−C−C−C dihedral angle, ϕ, of 35°) and anti (ϕ = 148°) conformations. Takayanagi et al.14 provided additional detail about the gasphase bithiophene torsional potential in the vicinity of the anti conformation, demonstrating the existence of a double-well potential based on LIF-excitation, hole-burning, and dispersed fluorescence spectroscopy. The experimentally derived potential exhibits equivalent energy minima at ϕ = 159° and 201° separated by a barrier of 25 cm−1. Notably, this barrier lies above the ground vibrational state, and so at low temperatures, isolated bithiophene is expected to adopt a nonplanar conformation. More recent work by Korter et al.15 used terahertz spectroscopy to probe the torsional potential of bithiophene in cyclohexane. Overall, they reported that the torsional potential of bithiophene in cyclohexane does not significantly differ from that of gas-phase bithiophene. The structure of crystalline bithiophene has also been characterized experimentally.16,17 In contrast to the structure in the gas phase and in solution, bithiophene adopts a planar configuration in a crystalline solid. The anti conformer is dominant, with syn bithiophene making up 15% of the crystal at 173 K; the syn conformer is not present in significant

I. INTRODUCTION Advances in organic electronic materials have proceeded at a rapid rate over the preceding decade, presaging the development of high-performance organic optoelectronic devices, field-effect transistors, and photovoltaics.1−7 Despite recent progress in this field, there are notable limitations of widely used organic electronic materials, and oligothiophenes (nT) in particular.6,8,9 The optoelectronic properties of organic conjugated polymers and oligomers are impacted by rates of charge transfer, rendering mobility, band gap, and ionization potentials as key determinants of material performance.10 The band gap depends on the extent of π-conjugation,9 and torsional defects can induce changes in physical and electronic properties of these materials that limit their performance in devices. In general, increased dihedral disorder reduces the average conjugation length of the backbone and increases the HOMO−LUMO energy gap.10 As Darling recently showed,11 the impact of these torsional defects may be mitigated in large nTs because charge transport may not be affected to the extent previous thought.2,12 Regardless, substituents commonly used to improve processability of these materials (e.g., alkyl chains, etc.) induce further deviations from planarity in oligo- and polythiophenes. In this regard, Bendikov and co-workers8 have shown that oligo- and polyselenophenes are considerably more rigid and tolerate a broader range of substituents while maintaining planar or near-planar configurations. The nonplanar structure of bithiophene has been documented experimentally both in the gas phase13,14 and in © 2012 American Chemical Society

Received: November 2, 2011 Revised: February 8, 2012 Published: February 16, 2012 2997

dx.doi.org/10.1021/jp210543z | J. Phys. Chem. A 2012, 116, 2997−3003

The Journal of Physical Chemistry A

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quantities at 133 K.16,17 The planarity of bithiophene in the solid state has been attributed to crystal packing interactions,9 highlighting the potentially significant role of interchain interactions on the torsional behavior of these conjugated oligomers. There have been several computational studies of the torsional behavior of isolated bithiophene.18,19 Raos et al.18 studied bithiophene using MP2, CCSD, CCSD(T), and B3LYP, finding that although these methods provided qualitatively similar potentials, there was a large spread in predicted barrier heights and locations of the syn and anti minima. Raos and co-workers18 reported that B3LYP performs comparably with MP2 given a sufficiently large basis set (aug-cc-pVTZ). Fabiano and co-workers19 showed that density functional theory (DFT)-predicted torsional potentials of bithiophene depend strongly on the functional. For oligothiophenes, there are several conceivable torsional motions, two of which have been studied previously.9−11,20 These prototypical torsional modes can be described as follows (Figure 1),

or packing forces in the solid state could induce twisting. Ultimately, they warned that such twisting defects of oligo- and polythiophenes need to be considered in the context of organic electronic materials. In 2008, Darling examined the effect of torsional motion about the central dihedral angle on the charge transport abilities of oligothiophenes.11 Surprisingly, Darling found that at 90° twists, predicted rates of charge transport in larger olgiothiophenes are nonzero. The following year, Darling and Sternberg10 again considered torsional motion about the central dihedral angle, demonstrating a strong dependence of computed torsional potentials on chain length and the presence of simple alkyl substituents based on computed twisting potentials in 2T, 4T, 6T, 8T, 10T, 12T, and 14T. Furthermore, they showed that geometric changes are not the cause of this dependence, which were instead attributed to electronic effects. Here, we study the torsional potentials of oligothiophenes primarily using DFT, focusing on the impact of neighboring chains. Torsions motions of individual oligothiophenes are explored, followed by investigations of the noncovalent interactions between oligothiophene chains and the impact of these interactions on computed torsional potentials. By studying prototypical torsional motions in model stacked oligothiophene dimers and higher order clusters, we can begin to bridge the gap between studies of isolated oligothiophene chains and the behavior of these systems in the solid state.

II. THEORETICAL METHODS Geometries were optimized primarily at the B97-D/TZV(2d,2p) level of theory. Torsions of oligothiophenes were defined in terms of the C−C−C−C dihedral angles ϕ (i.e., ϕ = 180° corresponds to anti, ϕ = 0° corresponds to syn configurations). To compute torsional potentials as a function of ϕ for both isolated and stacked chains, constrained optimizations were executed by holding the appropriate dihedral angles fixed and optimizing all other internal coordinates. All B97-D computations were performed using Gaussian09,21 and utilized density fitting. The accuracy of B97-D/TZV(2d,2p)22−24 predicted torsional potentials was verified through comparison with a CCSD(T)/augcc-pVTZ torsional potential for bithiophene (see Supporting Information Figure S1).25,26 These CCSD(T) energies were evaluated at MP2/aug-cc-pVTZ optimized geometries at 5° intervals between ϕ = 0 and 180°. As seen in Supporting Information Figure S1, B97-D/TZV(2d,2p) predicts a qualitatively correct torsional potential for bithiophene, overestimating the barrier separating the anti and syn conformations by about 0.8 kcal mol−1, and underestimating the energy of the syn conformer by 0.1 kcal mol−1, relative to the estimated CCSD(T)/aug-cc-pVTZ data. Counterpoise-corrected27 and density fit SCS-MP2/TZVPP interaction energies24,28 were also evaluated for the 6T dimers to confirm the B97-D/TZV(2d,2p) data (vide infra). Molpro201029 was used for the CCSD(T), MP2, and SCS-MP2 computations. Computations on a complex of seven 6T chains, with geometries taken from the 6T crystal structure,30 were executed using ONIOM, at the B97-D/TZV(2d,2p):UFF level.31,32 The central chain was computed at the B97-D/TZV(2d,2p) level of theory, whereas the surrounding 6T strands were calculated using UFF. The electrostatic environment of the outer chains were incorporated in the QM computations of the central chain via electronic embedding. To confirm that B97-D/TZV(2d,2p):UFF adequately describes the impact of a neighboring chain on the torsional potential of 6T, analogous computations were performed on a stacked 6T dimer. The ONIOM-computed potential for the

Figure 1. Two views of 6T along (a) helical, (b) ϕ1, and (c) wobble torsional modes.

where ϕi denotes the C−C−C-C dihedral angle between the ith and (i + 1)th thiophene ring: (1) uniform helical twisting of each dihedral angle (i.e., ϕ1 = ϕ2 = ... = ϕn−1 = ϕ) (2) twisting along a single dihedral angle, for either the terminal ring or a central ring (e.g., ϕ1 = ϕ; ϕ2 = ... = ϕn−1 = 180°) (3) alternating twisting (wobble) in which consecutive dihedral angles are equal but of opposite sign (i.e., ϕ1 = ϕ3 = ... = ϕn−2 = ϕ; ϕ2 = ϕ4 = ... = ϕn−1 = −ϕ) van Eijck, Johnson, and Kearley20 studied torsions about a single, terminal dihedral angle (ϕ1) in oligothiophenes using DFT, as well as the effect of packing interactions on the torsional potential of bithiophene. They reported that although the global minimum bithiophene structure exhibits a 153° twist, in the crystal environment it adopts a planar geometry (consistent with experiment16,17) and the force constant associated with torsional motion is increased 5-fold. Torsional potentials for 3T, 4T, and 6T were also reported,20 and it was shown that, for longer chains, the delocalization energy decreases, resulting in decreased torsional flexibility. Zade and Bendikov9 considered helical twists of 6T, 15T, and polyT, showing that these torsional motions induce considerable increases in the band gap at a very low energetic cost. Their results indicate that oligo- and polythiophene chains are exceptionally flexible, and they proposed9 that substituents 2998



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a function of the two C−C−C−C dihedral angles in 3T, relative to the all anti configuration (ϕ1 = ϕ2 = 180°) and evaluated at 15° intervals. This plot shows that the global minimum configuration for terthiophene has dihedral angles around 165° and 195°, which corresponds to the alternating twisting motion described above. One dimensional potential energy curves for simultaneous and stepwise torsional isomerization pathways on this two-dimensional energy surface are shown in Figure 2b. Simultaneous rotation of ϕ1 and ϕ2 is more energetically costly than stepwise rotations of individual dihedral angles. In particular, the transformation of 3T in an all-anti configuration to the all-syn conformation needs to surmount a barrier of only 4.3 kcal mol−1 if done in a stepwise fashion but requires 6.6 kcal mol−1 if rotations occur simultaneously. Similar results were found for the three-dimensional torsional potential for 4T; conversion between syn and anti conformations is most readily accomplished with stepwise rotations of individual dihedral angles, and the global minimum structure has dihedral angles that alternate around 180°. B97D predicted torsional potentials (per dihedral angle) are plotted in Figure 3 for the helical twisting of 2T−10T, considering

wobble-twisting of a 6T chain in the presence of a rigid 6T chain in an eclipsed stacked dimer qualitatively reproduces the torsional potential for the same system computed with B97-D applied to both chains (see Supporting Information Figure S2). The ONIOM-predicted potential overestimates the energetic cost of these torsional motions. As such, the computed torsional potentials for crystalline 6T will slightly overestimate the rigidity of these oligomers but should still provide a qualitatively correct picture of the torsional properties of crystalline oligothiophenes.

III. RESULTS AND DISCUSSION A. Oligothiophene Torsional Potentials. As discussed above, one can consider three prototypical torsional motions of an oligothiophene about the all anti conformation (Figure 1). We consider the torsional potential associated with each of these motions below. First, however, we consider the full twodimensional torsional potential energy surface of terthiophene (3T) to characterize likely torsional motions of an isolated nT chain. Figure 2a shows a relaxed 2-D potential energy surface as

Figure 3. Torsional potentials (kcal mol−1) for helical twisting per torsional angle for 2T−10T, relative to ϕ = 180°.

only even-numbered oligomers. The potentials all exhibit maxima at ϕ = 90/270°. Bithiophene is the only system considered for which the global minimum is not near 180°. For bithiophene, B97-D/TZV(2d,2p) predicts the global minimum conformer at ϕ = 160°, which is within 1° of the experimental gas-phase torsional minimum reported by Takayanagi and co-workers.14 As noted previously by Darling and Sternberg10 in the case of rotation about a central dihedral angle, and by van Eijck and coworkers20 for torsion about a terminal dihedral angle, the barrier for helical twisting per dihedral gradually increases with increasing chain length for helical twisting. This increase diminishes for the longer chains, and by 6T the predicted torsional barrier is within 0.2 kcal mol−1 of the barrier for 10T, per dihedral angle. Consequently, we focus on the torsional potentials of 6T, which should be representative of general oligothiophenes in this context. For each of these isolated oligomers, the potential is relatively flat in the region surrounding ϕ = 180°, and configurations spanning 30 to 40° in either direction along this helical twisting motion will be thermodynamically accessible at room temperature. Extension to polyT via use of periodic boundary conditions would likely lead to some changes in predicted potentials. However, the present results should provide qualitatively correct predictions

Figure 2. (a) Contour plot of two-dimensional torsional potential (kcal mol−1) for 3T, relative to ϕ1 = ϕ2 = 180°. (b) One-dimensional pathways for simultaneous and stepwise torsional changes from ϕ1 = ϕ2 = 180° to ϕ1 = ϕ2 = 0°. 2999



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rigid dimers, B97-D predicts that the staggered structure is favored over the eclipsed and T-shaped configurations by 2.0 and 2.9 kcal mol−1, respectively, whereas SCS-MP2 indicates that the staggered form lies 4.2 and 7.7 kcal mol−1 lower than the T-shaped and eclipsed configurations. The preference for the staggered arrangement is readily explained in terms of the favorable electrostatic interactions between the partially positively charged sulfur atoms and the π-cloud of the adjacent chain. The staggered configuration also maximizes dispersion effects relative to the T-shaped dimer. Upon relaxation, the structures of these rigid dimers change considerably, and the eclipsed dimer becomes the global energy minimum with a B97-D predicted interaction energy of −23.3 kcal mol−1 (SCS-MP2 predicts an interaction of −25.9 kcal mol−1). In both the staggered and eclipsed arrangements the chains are displaced parallel to one another, relieving the unfavorable electrostatic interactions between sulfur atoms present in the rigid eclipsed dimer. Moreover, in the relaxed staggered and eclipsed dimers, the 6T chains adopt wobbled configurations, with average dihedral angles of ±165.0° and ±168.8°, respectively. For the T-shaped dimer, the edge-chain distorts only slightly, whereas the face chain exhibits a significant distortion that combines both helical and wobbling motifs of approximately ±5° for each dihedral angle. The deviations from planarity in these optimized dimers confirm the conjecture of Zade and Bendikov9 that interchain interactions can readily induce torsional defects in oligo and polythiophenes. Indeed, the energetic costs of the distortion of these sexithiophene chains are only 0.1−0.8 kcal mol−1. The 6T trimer, tetramer, and septamer were also fully optimized, to gauge the extent to which additional neighboring interactions further perturb the equilibrium structure of 6T. As seen in Figure 6, the 6T chains adopt wobbled configurations in both the trimer and tetramer, with each sexithiophene curving toward the center of the cluster. In the 6T septamer, the central 6T chain is predicted to remain very close to planar, in accord with the structure of crystalline 6T.30 C. Torsional Potentials of Sexithiophene Dimers and Septamers. Finally, we consider the effect of interchain interactions on the three torsional modes of 6T. Previous studies have focused on helical twisting modes and torsions about a single dihedral angle, neglecting the wobble-type torsional defects that are apparent in optimized clusters of 6T (vide supra). Of primary importance is the impact of interchain π-stacking interactions on predicted torsional potentials, including the location of the energy minimum, the barrier to planarity, and the overall width of the torsional potential well.

of the impact of interchain interactions on the torsional behavior of both oligo- and polythiophenes. Computed potentials for the three prototypical torsional modes are plotted in Figure 4 for 6T. Unsurprisingly, for an

Figure 4. Torsional potentials (kcal mol−1) for helical twisting, wobble twisting, and ϕ1 twisting for 6T, relative to ϕ = 180°.

isolated 6T, rotation about a single dihedral angle is energetically facile compared to simultaneous rotation about each dihedral, regardless of whether these rotations occur along either helical or wobble modes. The torsional potentials for these two motions, which exhibit a barrier of nearly 20 kcal mol−1 for concerted transformation of an all anti to an all syn conformer, are qualitatively similar. However, the wobble potential surrounding ϕ = 180° is slightly broader than the helical twisting potential (vide infra). Moreover, the global minimum structure of 6T exhibits a slightly wobbled structure with alternating dihedral angles of ±178°, and this wobble mode is the most energetically favorable torsional motion involving simultaneous changes of all five dihedral angles for an isolated 6T chain. B. Noncovalent Sexithiophene Clusters. For noncovalent dimers of 6T, both rigid and fully relaxed eclipsed, staggered, and T-shaped configurations were considered, as shown in Figure 5. In the rigid dimers, only the interchain distance was optimized, with the facing rings located directly on top of one another. B97-D and counterpoise-corrected SCSMP2/TZVPP interaction energies are listed in Table 1. Both methods give qualitatively similar interaction energies. For the

Figure 5. Geometries of rigid (a, b, and c) and fully relaxed (d, e, f) 6T dimers in eclipsed (a and d), staggered (b and e), and T-shaped (c and f) configurations. 3000



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Table 1. B97-D/TZV(2d,2p) Interaction Energies (Eint, kcal mol−1, Relative to Separated Chains) and Interchain Distances (R, Å, Defined as the Distance between the Centers of Mass of the Two 6T Chains) for Rigid and Relaxed Noncovalent Dimers, Trimer, and Tetramer of 6T (Figures 5 and 6)a rigid dimer

T-shaped staggered eclipsed

relaxed

Eint

R

Eint

R

−15.3 (−18.1) −18.2 (−22.2) −16.2 (−14.5)

5.04 3.75 3.94

−17.2 (−16.3) −22.8 (−25.2) −23.3 (−25.9) −53.8 −85.2

4.90 3.47 3.52

trimer tetramer a

SCS-MP2/TZVPP predicted interaction energies (kcal mol−1) are shown in parentheses.

Figure 6. Fully optimized 6T trimer, tetramer, and septamer, all starting from the 6T crystal structure geometry.30

The impact of neighboring chains was studied primarily through two idealized models: (1) face-to-face eclipsed stacked dimers in which both chains are twisted in concert (dimer); and (2) a simple model of crystalline 6T in which a cluster of seven 6T chains was taken from the crystal structure geometry30 and the surrounding 6T chains held fixed while the central 6T was twisted (crystal). In Figure 7, computed torsional potentials are plotted for the three prototypical torsional modes for an isolated chain (Figure 7a), for a twisted dimer (Figure 7b), and in the model crystalline environment (Figure 7c). Predicted torsional potentials exhibit marked sensitivity to the environment. As discussed above, computed torsional potentials for isolated 6T chains are broadest for rotation about a single terminal dihedral angle, followed by wobble and helical torsional motions. The same trend is exhibited for 6T in the environment of the crystal, although with significantly larger force constants associated with torsional motion. Model stacked 6T chains exhibit a qualitatively different trend than the isolated chains and those in the crystal structure, with a global minimum structure in this eclipsed configuration exhibiting a helical twist (ϕ = ∼175°). This helically twisted minimum occurs at ∼5° deviations from planarity, and deviations of more than 10° from ϕ = 180° are energetically costly (Figure 7b). It should be noted that even though this helical twisted configuration is the global minimum for these perfectly eclipsed dimers, the corresponding relaxed helically twisted dimer (see Supporting Information Figure S3) lies 0.9 kcal mol−1 higher in energy than the relaxed dimer depicted in Figure 5d. Both ϕ1 and wobble motions exhibit exceptionally broad potentials, with comparable minima around ϕ = 160°. In other words, for eclipsed stacked dimers, large amplitude motions along ϕ1 and wobble modes are expected at room temperature. Although torsional potentials for the stacked dimers differ significantly from the isolated sexithiophene chains and crystalline model, these dimers should still be relevant to noncrystalline oligothiophene films.

Figure 7. Torsional potentials of 6T along helical, wobble, and ϕ1 modes for (a) isolated chains, (b) two chains twisted in concert, and (c) a twisted chain in the rigid crystal structure environment.

To understand the impact of cooperativity among torsional motions in the stacked 6T dimers discussed above, a model 3001



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the wobble mode, for which the concerted twisting of two chains does not enhance the stabilization afforded by deviations from planarity compared to a single chain. However, the minimum is shifted farther from planarity in the case of two twisted chains compared to twisting a single chain. Finally, for helical motions, twisting a single chain in the presence of a rigid planar chain leads to a single-well torsional potential with an energy minimum very close to ϕ = 180°, in contrast to the double-well potential predicted for the helical twisting of two 6T chains at once. Predicted torsional potentials are plotted in Figure 8 for each of the interacting model systems (isolated chain, stacked dimer, and crystal structure) for the helical, wobble, and ϕ1 torsional modes. For the helical twisting mode (Figure 8a), predicted potentials for the stacked dimer and crystal structure are significantly stiffer than that of a single chain. Interestingly, for torsional deviations beyond 10° from planarity, the potentials for the dimer and crystal converge, even though they differ considerably in the vicinity of ϕ = 180°. There is a strong preference for nonplanar 6T configurations in the stacked dimer, whereas for both the crystal and single strand a planar conformation is favorable. The wobble and ϕ1 motions behave in a similar manner to one another: for the stacked dimer there is a broad double-well potential whereas for isolated 6T and the 6T septamer, B97-D predicts a single-well torsional potential. However, the predicted force constant for these torsional motions in the crystal structure is increased by an order of magnitude compared to an isolated chain for the wobble and ϕ1 motions. The force constant in the case of helical twisting is enhanced by an even greater amount in the crystal environment as compared to the isolated 6T chain.

IV. SUMMARY AND CONCLUSIONS The impact of interchain interactions on three prototypical torsional modes of oligothiophenes has been studied at the B97-D/TZV(2d,2p) level of theory. Comparisons with a CCSD(T)/aug-cc-pVTZ torsional potential for bithiophene and SCS-MP2/TZVPP interaction energies for 6T dimers demonstrate that B97-D/TZV(2d,2p) provides a robust yet efficient means of studying both the torsional behavior of isolated oligothiophenes and noncovalent interactions between oligothiophene chains. For terthiophene, a 2-D torsional potential indicates that conversion of all-anti and all-cis conformations most readily occurs by flipping a single dihedral angle at a time. Moreover, for the oligothiophenes studied the global minimum structure exhibits a slightly wobbled conformation at the B97-D/TZV(2d,2p) level of theory, rather than the helically twisted configuration most often studied previously. Similarly, in stacked and T-shaped 6T dimers the individual chains adopt nonplanar, wobbled configurations, whereas in the environment of crystalline 6T the central chain prefers a planar configuration. For eclipsed stacked dimers, predicted torsional potentials change drastically, particularly for dimers in which both chains are twisted in concert. In this case, all torsional motions considered exhibit double-well potentials with significant deviations from planarity. In the case of torsional motion about the terminal dihedral angle and wobble-type motions, the predicted deviations from planarity are as severe as those exhibited by gas-phase bithiophene. In a model of crystalline 6T, computed torsional potentials are qualitatively similar to those for isolated 6T chains, but with force constants enhanced by at least an order of magnitude. Hence, in stacked dimers,

Figure 8. Torsional potentials of 6T along (a) helical, (b) wobble, and (c) ϕ1 modes for isolated chains, two chains twisted in concert (dimer), and a twisted chain in the rigid crystal structure environment (crystal).

system was constructed in which one 6T chain was fixed at the planar all-anti structure and the other strand twisted along each of the three torsional modes (see Supporting Information Figure S4). The resulting torsional potentials are highly asymmetric and deviate significantly from the corresponding potentials for isolated 6T or stacked 6T chains twisted in concert. Unsurprisingly, in these twisted-flat dimers, the torsional motions in which the sulfurs are moved away from the facing ring are energetically favored. Along the ϕ1 mode, the stabilization of the energy minimum relative to the planar structure is enhanced by cooperativity (i.e.: concerted twisting of both chains), but the predicted extent of deviation from planarity does not change significantly. The opposite occurs for 3002



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(21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, N. J.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö .; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, Revision A.1; Gaussian Inc.: Wallingford, CT, 2009. (22) Grimme, S. J. Comput. Chem. 2004, 25, 1463−1473. (23) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799. (24) Schafer, A.; Huber, C.; Ahlrichs, R. J. Chem. Phys. 1994, 100, 5829−5835. (25) Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M. Chem. Phys. Lett. 1989, 157, 479−483. (26) Kendall, R. A.; Dunning, T. H.; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796. (27) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553−566. (28) Grimme, S. J. Chem. Phys. 2003, 118, 9095. (29) MOLPRO is a package of ab initio programs written by H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz, P. Celani, T. Korona, R. Lindh, A. Mitrushenkov, G. Rauhut, K. R. Shamasundar, T. B. Adler, R. D. Amos, A. Bernhardsson, D. L. Berning. (30) Horowitz, G.; Bachet, B.; Yassar, A.; Lang, P.; Demanze, F.; Fave, J.-L.; Garnier, F. Chem. Mater. 1995, 7, 1337−1341. (31) Vreven, T.; Morokuma, K.; Farkas, O.; Schlegel, H. B.; Frisch, M. J. J. Comput. Chem. 2003, 24, 760−9. (32) Dapprich, S.; Komáromi, I.; Byun, K. N.; Morokuma, K.; Frisch, M. J. J. Mol. Struct.: THEOCHEM 1999, 461−462, 1−21.

oligothiophenes are predicted to exhibit large amplitude torsional motions with nonplanar torsional minima, whereas in crystalline 6T such torsional defects will incur a significant energetic penalty. The present results serve as a simple model of interchain interactions and demonstrate that the torsional potentials of oligothiophenes are sensitive to interchain interactions. Future studies of torsional defects in oligo- and polythiophenes should account for these interactions.

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ASSOCIATED CONTENT

S Supporting Information *

Additional figures of torsional potentials and optimized geometries and tables of absolute energies and Cartesian coordinates. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by ACS Petroleum Research Fund (PRF 50645-DNI6) and the National Science Foundation under CHE-1062840. We acknowledge the Texas A&M Supercomputing Facility for computational resources.

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REFERENCES

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